Range Voting and the Mathematics of Democracy

These are the slides for WDS lecture delivered at
VoComp, Portland OR 17 July 2007.
Earlier versions presented at Carnergie-Mellon University, Pittsburgh PA, 17-18 October 2006
and Univ. of Maryland (Baltimore) May 2007.

Abstract.
1. We argue "range voting" is the best single-winner voting method
among all commonly proposed alternatives. Measurements & estimates
indicate
that if adopted instead of the currently most-used system, "plurality voting,"
humanity's lot would improve by an amount comparable to or exceeding the
improvement got from switching from undemocratic forms of government to
democracy. Conservative estimate:
each day's delay in getting range voting
costs (in statistical sense) 5000 lives.

2. We argue (by analysing an explicit political strategy
to get it)
range voting is, in fact, an obtainable dream.

An elected partisan official in charge of supervising elections in 33 out of 50 states
(and in other states appointed by the governor – maybe even worse);

98% year-ahead predictability of all important races
(largest among democratic nations)
and uncontested state house races about a third of the time;

Massive two-party domination (over 99.5%)
causing opposing views to be almost completely blocked out of both power and the media;

Electoral college inspires candidates to cater only to "swing states," ignore rest;

Highly restrictive ballot-access laws in many states designed to ensure two-party (or one-party) domination not just in office but also on the ballot.
(Lieberman's run would have been illegal in 46/50 states.)

Voting systems

What is a "vote"?

System

A Vote

Plurality

Name one candidate then shut up ("Nader")

Borda & Condorcet

Rank ordering of all candidates ("Nader>Bush>Gore")

Approval

The set of candidates you 'approve' e.g. {Bush, Nader}

Range

Award score in 0-99 range to each and every
candidate, e.g. "Bush=50, Gore=99, Nader=99"

Systems most commonly mentioned in
political science literature illustrated by example:

#voters

Their Vote

4

A>D>E>C>B>F

3

B>E>D>F>C>A

2

C>B>E>D>F>A

1

D>C>F>A>E>B

1

F>C>E>D>B>A

An 11-voter, 6-candidate election (candidates A,B,C,D,E,F)

Plurality: A wins (most top-rank votes with 4).
Plurality+Runoff among top two: B wins over A in the runoff, 6-to-5.
Instant Runoff (IRV): C wins
(eliminate E, D, F, and B in that order – doesn't matter which way you break
DF tie – then C beats A in final round 7 to 4).
IRV repeatedly deletes the candidate with fewest
top-rank votes, then the remaining one wins.
Borda: D wins.
(D's Borda score is 16+9+4+5+2=36 versus E with 12+12+6+1+3=34 and
with lower scores for A, B, C, and F.) In the Borda system a candidate gets awarded
0 points if ranked last, 1 if ranked second-last, 2 if... and the candidate
with the greatest score-sum ("Borda count") wins.
Condorcet: E wins. (Since E pairwise-beats each other candidate, e.g. beating
A 6:5, B 6:5, C 7:4, D 6:5, and F 9:2.)
Approval Voting:
If all the red candidates are "approved," then F wins with
7 approvals (versus A=4, B=5, C=3, D=6, E=5).

And with 0-99 Range Voting,
it would in fact be possible to make any of the 6
candidates win,
depending on how the voters chose the scores compatibly with the orderings above.
In Range Voting each voter awards a score from 0 to 99 to each candidate;
greatest average score wins.
(Fancier rules allow also scoring a candidate with
X = intentional blank = "no opinion" – only numerical scores incorporated
into averages.)

Arrow impossibility theorem & Nobel causes 50 year timewaste

K.J.Arrow's (1950) theorem states that no voting method
can satisfy following short list of conditions:

#voters

Their Vote

8

B>C>A

6

C>A>B

5

A>B>C

B wins? Drop C then A wins

Is no dictator.

If every voter prefers A to B then so does group.

Relative positions of A and B in the group ranking depend on their
relative positions in the individual rankings, but do not depend on the
individual rankings of any irrelevant alternative C.

"This discovery was a major factor in Arrow winning the Nobel Prize in Economics."

Commonly heard: "Arrow's theorem shows that no 'best' voting system exists."
"Proof":
By Arrow, for every voting system, including the putative "best" system B,
exists an election which makes it look bad. Construct system A which looks good in that situation.
Then A is "superior" to B so B cannot be best. Q.E.D.

That all is wrong.Range voting satisfies all three
criteria, accomplishing the "impossible"!

(Reinforcement:
I have a paper
in which I construct "universal counterexamples"
which make every voting method based on finite set of
vote-types look bad [min-utility winners]
while range voting [continuum infinity of vote-types] looks
good [max-utility winner].)

Bogusness. "Property based" thinking
misled all of political science for 50 years.

Three ways to (try to) seek a best voting system

Pros: Real; right sample space.
Cons[Historical]: Often hard to assess
how "good" different election results were or would have been
and what results "would" have occurred
had other election method X had been used instead.
(And subjective. And you'll be accused of bias.)
Also, still not really correct sample
space (since space might change over time with new X...).
Cons[Paid subjects]:
Very expensive. Not really real.
Cons[Both]: Little data ⇒ low statistical significance ⇒ few results.
And people lie to pollsters.

2. Find planet; create eusocial lifeform that needs to conduct elections
as important part of life-cycle; better decisions via the elections ⇒ more fitness;
put on planet; wait 20-200 million years; see
what voting system Darwinian evolution comes up with.

Pros: Real (arguably more real than with humans). Lots of data ⇒ high significance.
Cons: Spare planets unavailable in local drug store.
Pros: Already been done at least twice on this planet (social insects)!! Hundreds of
trillions of very-important-to-the-insects elections so far! All voting systems
considered (in some sense).

Pros: Large amounts of data ⇒ statistical significance is no problem.
Artificial cyber-voters better than humans:
Can read their "minds" to
find their true desires unpolluted by lies
(measured in standard "happiness units" too).
Cons: Computer results out = only as good as the assumptions & models in.
Only try voting systems you try, not all possible.
Pros:
Can try large number of assumption sets & models. If so lucky that
in all of them, one voting method robustly is best, convincing.
Con: If not so lucky – some methods best in this model, others best in that ⇒
bummer.

What is Bayesian Regret?

Each voter has a personal
"utility" value for the election of each candidate.
(E.g, if Nixon elected, then Jill Voter acquires -55 extra lifetime happiness units.)
In computer simulation, "voters" & "candidates" are artificial,
and the utility numbers are generated by
some randomized "utility generator" and assigned
artificially to each candidate-voter pair.

Now the voters vote, based both on their private utility
values, and (if strategic voters)
on their perception from "pre-election polls"
(also generated artificially within the simulation, e.g. from
a random subsample of "people") of how
the other voters are going to act.
(Note. Some people here have gotten the wrong impression
that this is assuming that voters will be "honest" or that we are
assuming that honest range voters
will use candidate-utilities as their candidate-scores. Neither impression is correct:
These assumptions are not made.)

Election system E elects some winning candidate W.

The sum over all voters V of their utility for W, is
the "achieved societal utility."

The sum over all voters V of their utility for X,
maximized over all candidates X, is
the "optimum societal utility" which would have been
achieved if the election system had magically chosen the
societally best candidate.

The difference
between 5 and 4 is the "Bayesian Regret"
of the election system E, at least in this experiment.
It might be zero, but if E was bad or if this election was unlucky for E, then
it will be positive because W and X will be different candidates.

Redo steps 1-6 zillion times
(i.e. do zillion simulated elections) to find
average Bayesian regret of election system E.

Comments:
The Bayesian regret of an election system E may differ if we

Vary the number of voters,

Vary the number of candidates,

Vary the kind of "utility generator" (e.g. could be based on different numbers of "issues"
with different methods for generating the locations of the candidates in "issue space"),

Use different kinds of assumed "voter strategy", or

Put different amounts of "voter ignorance". (*)

(*) Can put in
voter ignorance by artificially adding random noise to
voter's private utility values, and then make voters act
based on distorted values. Higher amplitude
noise ⇒ more ignorance.

∃ at least 5 different "knobs" to "turn" on our
machine for measuring Bayesian Regret of elctn method E.

Measured Bayesian regrets for about 30 different election methods.
720 different "knob setting" combinations tried.
Amazing result: in all 720 scenarios, range voting
was best (had lowest Bayesian regret, up to statistically insignificant
noise). We repeat: RV best in every single one
of those 720 with either honest or
strategic
voters, regardless of ignorance-level, #candidates (3-5),
#voters (5-200), #issues (0-∞)
etc.

Warning: Table makes it appear Borda is second-best after
range. But in fact the full study considers hundreds of tables like this,
& in many of them, Borda is not second best, in fact in many
it's way down in the rankings. The question of which system is second best
has no clear answer – some better in some kinds
of election situations, others in others.

A second BR study (2006)

Less ambitious (but simpler and more reproducible)
study: only did the "one-dimensional 3-candidate left-middle-right"
political scenario, and very few kinds of voter strategy.
But attempted exhaustive set of 623700
configurations, essentially completely covering that space.

During this [the 20th] century's wars, there were some 38 million battle deaths,
but almost four times more people – at least 170 million –
were killed by governments for ethnic, racial, tribal,
religious, or political reasons. I call this phenomenon
democide, and it means that authoritarian and totalitarian
governments are more deadly than war.
–
R.J.Rummel
(prof. Emeritus, U.Hawaii),
in his book Death by Government

Rummel on his democide statistics website
gives corrections now finding the democide body count during 1900-1999 to be
262,000,000, which is six times the war dead and equiv. to 7200 killed per day.

3. Government waste:
Economist Martin Bailey estimates US Govt spending is 50% waste (e.g. same power military could
be got with half the money, etc.); detailed tabulation in his book.
That 50% is $1.1 Trillion/year, which is equivalent to 4.4 million lives per year,
i.e. 12050 lives/day.
(At rate of 1 life=$250,000 earned per world-average life).

Gazillionaire donors: listen up!

Range voting gives you more "bang" for your buck than almost any other philanthropic option.
Maybe the most lives saved for this small an effort.
And you can be in the steep part of the learning curve by seeding the start of
the RV movement, getting huge leverage for your money.
(More details)

But democracy increases GDP in peculiar way (pictured):
increases in Barro's political rights index from 0 to 5.6 on a scale of 0-10
(yielding a moderate level of freedom and democracy)
increased GDP growth rates additively by 2.6%
but a further increase in the index from 5.6 to 10
retarded growth by negative 1.6%.

All of Barro's causative
factors (listed) cause approximately equal additive effects on predicted
real-GDP-growth-rate,
namely about 2-5% each. That is, having the optimum level 5.6 of political rights
causes about 2.6% higher (additively) annual GDP growth rate than the pessimal
level 0; countries about one standard deviation above usual in education levels are
predicted to have about 3% higher than usual annual-GDP-growth;
etc.

Correlation≠certainty so
democracy does not force a good economy. E.g, China doing better than India.

Why that peaking and downturn?

Barro
ideologically tries to explain by postulating:
more democracy ⇒ more government income redistribution ⇒ hurts growth.
But attackable because
Barro's fit already had incorporated government
expenditures
as different predictor; democratization was only being fit to
unexplained part of the GDP growth above and beyond that explainable
as result of government outlays.
Barro partly
defends by saying that government transfer payments were not
held constant.
But, assuming Barro has
idea that transfers aim toward equalizing wealth,
he is exactly wrong about its economic effect:
the Deininger-Squires 1998 World Bank cross-country
study
found that greater initial inequality is strongly negatively correlated
to future economic growth!

In other words, the "trickle down theory" often associated with Ronald Reagan
is wrong.
According to
George R. G. Clarke:
More Evidence on Income Distribution and Growth,
J. Development Economics 47,2 (Aug. 1995) 403-427,
"This conclusion is robust across different inequality measures,
and to many different specifications of the growth regression.
Furthermore, inequality appears to have a negative effect on
both democracies and non-democracies.
Interaction terms between inequality and regime type, when included in the
base regression, do not affect the sign or significance of [this]."
So this seems to settle the matter. (However, to completely clarify matters,
it would be good to put transfer payments into Barro's fit also, to see what happens.
And two other good predictors to try inserting would be a country's winter temperature
and the "centralization fraction" of its government
[See A.Lijphart: Democracies 1984 table 10.2 page 178].)

Two other possible explanatory hypotheses:
(more supported than Barro's):

More democracy ⇒ dumb people make more dumb decisions ⇒ worse economic growth.

Even smart people make dumb decisions if the "decision-making algorithm" is "a poor
voting system." If so, then replacing voting system with better one, e.g.
range voting, would yield
big economic growth win, and that peak & downturn
might be avoidable – the curve instead would just keep going up!

Which? (Or both?)
If b ⇒ economic growth win attainable by switch to
Range or other better Voting
appears greater than attainable by altering any other factor identified by Barro
(also seems much easier to change voting system than to alter
any of those other factors).

Why is RV best? (Aside from "because my computer says so.")

Other computers say so too.

Quick picture:

RV ≈same as Approval if strategic voters & better if honest voters.

RV way better than Borda if strategic & somewhat better if honest voters.

Not initially so obvious versus Condorcet, but... (a) if enough voter honesty,
then RV can avoid "tyranny of majority" surpassing Condorcet and every other usual method;
(b) if strategic voters, can prove theorem
that RV yields (under reasonable assmptns)
the honest-voter Condorcet winner!

Some theorems saying range voting reacts mildly to strategic voting

Avoids favorite betrayal:
In range voting, there is never a strategic reason to give your favorite a non-top score.
(Unlike: IRV, Condorcet, Borda, Plurality, where favorite-betrayal often advisable.)

Semi-honesty:
In range voting, if you know all other votes (or in a ≤3-candidate election
even if you have only partial knowledge of the other votes),
then there is always a strategically-optimal
"semi-honest" threshold-style vote, where create a "threshold" T and
give all candidates better than T score=99, all others score=0.
(Unlike: IRV, Condorcet, Borda, Plurality, where it can happen
that every honest & semi-honest vote is non-strategic.)

Pleasant surprise theorem:
Suppose each voter chooses T=their expectation of the value of the winner.
Then: the range-winner will maximize the number of voters who are "pleasantly surprised"
(result exceeds expectations). That's an optimality property related to,
but not identical to, minimizing Bayesian regret.

Range⇒Condorcet theorem:
Suppose each chooses T
somewhere between candidates C and A, where C and A are viewed
as the two most likely to win. If one of C or A is an honest-voter Condorcet
winner, then he will also be the range-winner. (Suggests that in practice,
Condorcet cannot have much advantage over range.)

This favorite-betrayal example very important because, once voters understand
exaggerating their stances on the apparent-frontrunners can be necessary to
prevent "greater evil"s victory, strategic voting is guaranteed, often causing
"third parties" to tend to die out (since the strategic voters won't
"waste their vote" on honest-favorite third-party candidates like N whom they perceive as
having "no chance of winning").

Condorcet: A should win.
(A also wins under IRV voting method.)
Borda: no, B should win!
Who really should win? Good question.

How would range voting handle this?
RV allows voters to say how much they
prefer B over A (or whoever). Quantitatively.
Really, Borda or Condorcet are both right – but depending
on intensity-of-preference information unavailable to their voting methods,
but available to range voting. So this example illustrates an advantage of range voting
over both previous voting systems.

Cloning – bad news for Borda & Plurality

Several near-identical "clone" candidates run.
Plurality voting: they split the vote and all lose.
The very popularity of a view can cause its defeat!Borda voting (basically): enough clones ⇒ opposite effect ("teaming");
assured victory!

Obviously, Mush wins this one.

#voters

their vote

51

Mush

49

Bore

But now, if Bore has numerous clones (call them Bore1,
Bore2, and Bore3 in decreasing order of attractiveness)
then the Borda vote would give Bore1 an easy victory:

#voters

their vote

51

Mush > Bore1 > Bore2 > Bore3

49

Bore1 > Bore2 > Bore3 > Mush

(totals)

Mush=153, Bore1=249, Bore2=149, Bore3=49.

Cloning the Bores ⇒ huge advantage! Boring party can just arrange for mucho
Bores to enter the race & totally Boring!
Of course, Mushites could try to defeat that by intentionally lying in their
votes by ranking
Bores in opposite of true order, to try to cancel out
the Borites and make Mush win.
But this strategy causes them to be massively dishonest in
their votes and risk not only a Bore-victory, but in fact a victory
by the worst of the Bores! (Which would in fact happen if the Borons
counterstrategized by also being dishonest in their Bore-orderings!)
Crazy!

Mushites: fight by nominating own clones,
Mush1, Mush2, Mush3, and Mush4,
so they'll win.
Bores: countersponsor more clones
Bore4, Bore5, Bore6.
Etc. War of clone armies.
All about gall, little to do with what voters actually want.

Has caused parties to intentionally aid opponents of
their point of view ("helping a spoiler")! And it also has (more often) caused
parties to intentionally hurt allies of their point of view!

DH3 pathology – bad news for Borda & Condorcet

Common scenario:
Whenever there are 3 rival contenders A,B,C plus one or more "dark horses" D
that all agree are worthless no-hopers:
In Borda & most Condorcet systems it pays for each for the 3 factions
to dishonestly rank D "above" the other two rivals.
(Strategic justification: Whichever faction votes honestly, guaranteed to lose the election.
Condorcet systems with equal rankings allowed? Ranking D co-equal-last like A>B=C=D
is not good enough strategy; only "full force" dishonesty A>D>B>C is strategic.)

IRV = bad

I.
IRV leads to 2-party domination (but the closely related
top-2-runofftwo-round system
leads to ≥3 parties).
(For voters too dumb to appreciate this, often they'll probably just
exaggerate ("Bush is the best! Gore is the worst" out of dumbness anyhow; same effect
as being smart.)

At right, suppose 8 voters in bottom faction cleverly (but dishonestly)
switch their top-2 preference order.
Then
N is eliminated in the first round,
and then in the second round G wins over B 73-to-27.
From those 8 voters' point of view, this was an improvement.
Betraying Nader Pays in IRV. Voting Nader causes spoiler effect still in IRV.

Winner=Loser reversal paradox in IRV

#voters

their vote

9

B>C>A

8

A>B>C

7

C>A>B

II.
In this 24-voter IRV election, A wins after C is dropped.
But now suppose every voter reverses his preference order (now
attempting to choose worst rather than best).
In that case A still wins after B is eliminated.
I.e. IRV contradicts itself; IRV's unambiguously
"best" candidate A is here
the same as its "worst"!

Also illustrates bizarre kind of strategic voting: Suppose
3 of the B>C>A voters reverse their votes to A>C>B (or alter them to A>B>C; that also works).
Then B is eliminated whereupon C wins 13-to-11 over A.
The raising of A from bottom-to-top in their vote caused A to lose –
and voting maximally dishonestly as though they were suicidally
trying to elect the worst
candidate, was actually optimal strategy!

Also illustrates "no show paradox":
If those three B>C>A voters had simply refused to vote,
then C would have won (an improvement in their view).
Different way of saying the same thing:
these three voters' decision to cast an honest A-last vote
caused A to win.

"Secondary effects"

"Primary" effect (reckoned using Bayesian regret):
just who wins the election & how
much utility that is. "Secondary" effects exert themselves over historical
time in sequence of many elections. When these also reckoned, RV looks even better...

One-party domination:
98% predictability
in contemporary USA.
(One reason is gerrymandering... by which one party can stay permanently in power
even if only 25+ε% support.)

Cash:
is extremely important in plurality voting, but perceived to be less so in other systems
e.g. plur+top-2-runoff. Why? Need to demonstrate you are one of the top-2 "frontrunners,"
i.e. create illusion of winnability, otherwise not worth wasting vote on you.
That's expensive. (Educating about issues: cheap.)

Media:
Pays no attention to third-party views (no motivation; they're not news).
Media "lapdogs" unquestioningly accept politicians' BS without much
critical examination (because with 2-party and 1-party domination, politicians
are in monopoly position to cut off media lifeblood; with multiparties no
such info monopoly)

Lack of congressional oversight:
For most of about 8 years, Democrats in Congress haven't been able to subpoena anyone.

Rubberstamped agency heads & judge appointments:
In votes for court of
appeals nominees, Republican Senators during the Bush administration (during
majority control) produced 2703 votes for the nominee as opposed to only a single
"no" vote (cast by Trent Lott against judge Roger Gregory, the
first Black ever appointed to this position).

Bush appointed Joseph Allbaugh as head of FEMA in 2001, although Allbaugh had no
expertise or experience handling emergencies, but rather had been
then-Texas-Governor Bush's chief of staff & campaign manager for
Bush-Cheney nationwide campaign.
(Allbaugh had B.S. in political science from Oklahoma State University.)
In 2003, Allbaugh replaced by Michael D. Brown –
Former estate and family lawyer and bar examiner.
The Boston Herald reports that Brown was "fired from his last private-sector job, overseeing horse shows... after a spate of lawsuits over alleged supervision failures... `He was asked to resign,' Bill Pennington, president of the IAHA at the time, confirmed last night."

Pork & earmark game-playing:

FEMA (Federal Emergency Management Agency),
in report well before both Hurricane Katrina and the 9/11 attack, summarized top
3 threats to the USA as a terrorist attack on New York, major earthquake in
San Francisco and hurricane strike on New Orleans.
But Bush and Congress by bipartisan budget vote
turned down
Louisiana's requests for mere tens of millions
per year to protect
New Orleans.
New Orleans contained
urban & poor people, many blacks, hence a high% Democrat voters;
Louisiana had democrat senator,
& starting in 2004, a democrat governor.

1992 US Pres. Election [analysis
NES data by Steven J. Brams
& Samuel Merrill III
Politics and Political Science 27,1 (March 1994) 39-44],
the vote totals again would have been tremendously altered with
approval voting (although finish order would not have changed) again
illustrating tremendous distortionary penalty faced by third-party
candidates under plurality system.

And in the 1980 US Presidential Election, according to analysis
based on many polls in ch. 9 of
Brams & Fishburn's book,

1992 results:

Candidate

Plur

AV

Clinton(Dem)

43.0

55

Bush(Rep)

37.4

49

Perot

18.9

42

Anderson probably actually would have come in second behind Reagan but ahead
of Carter, under approval voting, whereas under plurality voting he was far
in third place with under 7% of the votes.
Again illustrates the tremendous distortionary penalty faced by third-party
candidates under the undemocratic plurality system.

Psychology-aided effects

RV has some further advantages perhaps not mathematically explainable, but which instead are
experimental facts that are consequences of human psychology:

Range: 0.026% spoilage rate (per candidate) observed in our exit poll; 99.5% confidence
that range rate per canddt is at least twice as small as USA's plurality error rate of 1.8%.
Similar results in French study.
One reason:
RV & AV: every way to fill in scores is legal. IRV & plurality: not so.
Another(?): range & approval voters repeatedly do the same operation many times in each race,
causing them to be more careful and inherently self-checking. (Plurality: do it only once.)

Cornell U. prof. Walter Mebane Jr. analysed
ballot-level data from the NORC Florida ballots project and ballot-image files,
concluded that "If the best type of vote tabulation system
used in the state in 2000 – precinct-tabulated optical scan
ballots –
had been used statewide then [due to inequities in the distribution
of voting machines & settings of those machines]
Gore would have won by more
than 30,000 votes."
[
W.Mebane Jr.:
The Wrong Man is President! Overvotes in the 2000 Presidential Election in Florida,
Perspectives on Politics 2,3 (September 2004) 525-535]

This happening not only at the county level,
but also district by district statewide.
268 Duval precincts: fluke result due to random fluctuations?
Not.
Enough to swing the Bush-Gore election result in Florida (which was decided by
an official margin of only 537 votes)? Easily.
(Palast maps,
caption)

Tactical reasons to prefer Range Voting

1. Range Voting works, simply, on every (plurality) voting machine!

Mathematically: ∃ transformation
of one C-candidate (0-9 plus X) range voting election
to 11C artificial "plurality elections." In some cases, this is easy and convenient from
the viewpoint of voters (optical scan machines) in others it is less convenient (which is
why we would prefer to have purpose-designed range-voting machines) – but it
always works, easing transition worries greatly.

Demo:

Award each candidate a numerical score from 0 to 9.
Advise giving your favorite candidate 9 and the worst one 0.
If you intentionally wish to express no opinion about that candidate, then please
do not select any score for him – equivalently leave the default
"X" choice selected;
only numerical scores will be incorporated into the averaging.

Both the Dems & Repubs (at all levels: rank-and-file members countrywide
and Iowa-wide, Iowa state party leaders, national party leaders),
are motivated to want to use
range so they can get a better presidential nominee,
and seem in favor of reform, and get free publicity; Iowans may also
be in favor of change since many may believe Kerry (or Bush) was a mistake by them.

"Random normal elections": How often do the range & plurality winners agree?

#candidates:

C=2

3

4

5

8

10

15

20

50

100

200

5123 voters

100%

73%

61%

52%

38%

32%

24%

19%

8%

4%

2%

Third parties want range voting and their supporters constitute at least 1% and
arguably as much as 40% of society. They could swing the election. It is
worth catering to their desires, especially when it also benefits everybody
else including the major parties and all USA-wide.

Leads to voter education, reform, free good publicity beneficial for all involved,
and better US presidential candidates.

Social Insects

Honeybee (Apis Mellifera) swarms
(each spring) and the 3mm-long eusocial ant
Leptothorax Albipennis (after nest destruction)
both use range voting to decide on the location of their new nest.

Problems bees face:
Tiny brains. Can they do "addition," "division," and "averaging"?
If so, can they communicate results reliably? What if some bees mentally defective
or miscommunicate? How to reach a swarm-wide consensus? How to do it quickly?
"Robust log-time parallel algorithm"...

Eventually the faction advocating the site with greatest average score, dominates
population (even if initially small; higher exponential wins out over constant factor).

"Quorum rule" that it ain't over until enough votes are in.

How good are they?
Swarm: 2000-20000 bees.
≥1015 elections so far.
Usually find ≈20 different housing options within about 100 km2,
and ≈90% of the time, bee swarm succeeds in selecting (what
appears to entomologists to be) best one.

Ants:
The most successful macroscopic land animals (15-20% of all land animal biomass?!).
200 Myr old.

Splitline algorithm to get rid of gerrymandering

Shortest splitline
algorithm eliminates gerrymandering. Basically: find
shortest line splitting state into two parts with right population ratios,
then continue recursively.
This produces better district maps for less cost than present methods and is completely unbiased.
Blue map shows Massachusetts as gerrymandered to have 100%
Democratic congressmen,
versus districts that would have been produced by splitline.